Correctness in Computer Programs and Mathematical Proofs

The standard
of correctness and completeness necessary to get a computer program to work at
all is a couple of orders of magnitude higher than the mathematical
community’s
standard of valid proofs. Nonetheless, large computer programs, even when they
have been very carefully written and very carefully tested, always seem to
have
bugs.

I noticed that mathematicians are often sloppy about the scope of
their symbols. Sometimes they use the same symbol for two different meanings,
and you have to guess from context which on is meant.

This kind of sloppiness generally doesn't have an impact on the validity of
the ideas that are communicated, as long as it's still understandable to the
reader.

I guess on reason is that most mathematical publications still stick to
one-letter symbol names, and there aren't that many letters in the alphabets
that are generally accepted for usage (Latin, Greek, a few letters from
Hebrew). And in the programming world we snort derisively at FORTRAN 77 that
limited variable names to a length of 6 characters.